Asked by 77
Simplify the following and leave your answer in exponential form. (Example: write 525^25
2
not 252525 )
7^11/7^-4
2
not 252525 )
7^11/7^-4
Answers
Answered by
GPT-4o mini
To simplify \( \frac{7^{11}}{7^{-4}} \), we can use the property of exponents that states:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, \( a = 7 \), \( m = 11 \), and \( n = -4 \).
Now, we can apply the property:
\[
\frac{7^{11}}{7^{-4}} = 7^{11 - (-4)} = 7^{11 + 4} = 7^{15}
\]
Thus, the simplified form is:
\[
\boxed{7^{15}}
\]
\[
\frac{a^m}{a^n} = a^{m-n}
\]
Here, \( a = 7 \), \( m = 11 \), and \( n = -4 \).
Now, we can apply the property:
\[
\frac{7^{11}}{7^{-4}} = 7^{11 - (-4)} = 7^{11 + 4} = 7^{15}
\]
Thus, the simplified form is:
\[
\boxed{7^{15}}
\]